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Four Color Problem

Some of you may know of a theorem called the Four Color Theorem. Many of you may not. It has the distinction of being the first major theorem to be proved using a computer. And thus, to many mathematicians the proof is not accepted since faith must be placed in the computer for the result and there is a complete lack of elegance to the proof. After all, “a good mathematical proof is like a poem . . . this [proof] is a telephone directory!” – Wikipedia

The theorem states that any plane separated into regions, such as a map of countries or states, can be colored with only four colors, such that no adjacent regions have the same color. Now, if you accept this a fact (which you most certainly should), that still leaves open the question of how to perform the coloring. Sure, a coloring using only four colors exists but finding it is another matter. Try it for yourself: